Homographies are among the most prevalent transformations occurring in geometric computer vision and projective geometry, and homography estimation is consequently a crucial step in a wide assortment of computer vision tasks. When working with real images, which are often afflicted with geometric distortions caused by the camera lens, it may be necessary to determine both the homography and the lens distortion-particularly the radial component, called radial distortion-simultaneously to obtain anything resembling useful estimates. When considering a homography with radial distortion between two images, there are three conceptually distinct configurations for the radial distortion; (i) distortion in only one image, (ii) identical distortion in the two images, and (iii) independent distortion in the two images. While these cases have been addressed separately in the past, the present paper provides a novel and unified approach to solve all three cases. We demonstrate how the proposed approach can be used to construct new fast, stable, and accurate minimal solvers for radially distorted homographies. In all three cases, our proposed solvers are faster than the existing state-of-the-art solvers while maintaining similar accuracy. The solvers are tested on well-established benchmarks including images taken with fisheye cameras. A reference implementation of the proposed solvers is made available as part of HomLib11https://github.com/marcusvaltonen/HomLib.

In this paper, we challenge the current view on state-of-the-art deep learning-based methods for compressing wireless channel state information and show that traditional methods can be highly competitive on commonly used open-source benchmarks. We show that basic signal processing methods can offer superior performance and argue that the datasets and the metrics used in measuring performance give a skewed impression of the applicability and extendibility of the methods proposed in the literature today.

Low rank inducing penalties have been proven to successfully uncover fundamental structures considered in computer vision and machine learning; however, such methods generally lead to non-convex optimization problems. Since the resulting objective is non-convex one often resorts to using standard splitting schemes such as Alternating Direction Methods of Multipliers (ADMM), or other subgradient methods, which exhibit slow convergence in the neighbourhood of a local minimum. We propose a method using second order methods, in particular the variable projection method (VarPro), by replacing the nonconvex penalties with a surrogate capable of converting the original objectives to differentiable equivalents. In this way we benefit from faster convergence.The bilinear framework is compatible with a large family of regularizers, and we demonstrate the benefits of our approach on real datasets for rigid and non-rigid structure from motion. The qualitative difference in reconstructions show that many popular non-convex objectives enjoy an advantage in transitioning to the proposed framework.1

In this paper we present a novel algorithm for onboard radial distortion correction for unmanned aerial vehicles (UAVs) equipped with an inertial measurement unit (IMU), that runs in real-time. This approach makes calibration procedures redundant, thus allowing for exchange of optics extemporaneously. By utilizing the IMU data, the cameras can be aligned with the gravity direction. This allows us to work with fewer degrees of freedom, and opens up for further intrinsic calibration. We propose a fast and robust minimal solver for simultaneously estimating the focal length, radial distortion profile and motion parameters from homographies. The proposed solver is tested on both synthetic and real data, and perform better or on par with state-of-the-art methods relying on pre-calibration procedures. Code available at: https://github.com/marcusvaltonen/HomLib.1

In this paper we study the convex envelopes of a new class of functions. Using this approach, we are able to unify two important classes of regularizers from unbiased non-convex formulations and weighted nuclear norm penalties. This opens up for possibilities of combining the best of both worlds, and to leverage each methods contribution to cases where simply enforcing one of the regularizers are insufficient. We show that the proposed regularizers can be incorporated in standard splitting schemes such as Alternating Direction Methods of Multipliers (ADMM), and other sub-gradient methods. This can be implemented efficiently since the the proximal operator can be computed fast. Furthermore, we show on real non-rigid structure from motion datasets, the issues that arise from using weighted nuclear norm penalties, and how this can be remedied using our proposed prior-free method.

In this paper we consider a collection of relative pose problems which arise naturally in applications for visual indoor UAV navigation. We focus on cases where additional information from an onboard IMU is available and thus provides a partial extrinsic calibration through the gravitational vector. The solvers are designed for a partially calibrated camera, for a variety of realistic indoor scenarios, which makes it possible to navigate using images of the ground floor. Current state-of-the-art solvers use more general assumptions, such as using arbitrary planar structures; however, these solvers do not yield adequate reconstructions for real scenes, nor do they perform fast enough to be incorporated in real-time systems. We show that the proposed solvers enjoy better numerical stability, are faster, and require fewer point correspondences, compared to state-of-the-art solvers. These properties are vital components for robust navigation in real-time systems, and we demonstrate on both synthetic and real data that our method outperforms other methods, and yields superior motion estimation.

Fast and accurate homography estimation is essential to many computer vision applications, including scene degenerate cases and planarity detection. Such cases arise naturally in man-made environments, and failure to handle them will result in poor positioning estimates. Most modern day consumer cameras are affected by some level of radial distortion, which must be compensated for in order to get accurate estimates. This often demands calibration procedures, with specific scene requirements, and off-line processing. In this paper a novel polynomial solver for radially distorted planar motion compatible homographies is presented. The proposed algorithm is fast and numerically stable, and is proven on both synthetic and real data to work well inside a RANSAC loop.

This paper presents a novel polynomial constraint for homographies compatible with the general planar motion model. In this setting, compatible homographies have five degrees of freedom-instead of the general case of eight degrees of freedom-and, as a consequence, a minimal solver requires 2.5 point correspondences. The existing minimal solver, however, is computationally expensive, and we propose using non-minimal solvers, which significantly reduces the execution time of obtaining a compatible homography, with accuracy and robustness comparable to that of the minimal solver. The proposed solvers are compared with the minimal solver and the traditional 4-point solver on synthetic and real data, and demonstrate good performance, in terms of speed and accuracy. By decomposing the homographies obtained from the different methods, it is shown that the proposed solvers have future potential to be incorporated in a complete Simultaneous Localization and Mapping (SLAM) framework.

In this paper we consider trajectory recovery for two cameras directed towards the floor, and which are mounted rigidly on a mobile platform. Previous work for this specific problem geometry has focused on locally minimising an algebraic error between inter-image homographies to estimate the relative pose. In order to accurately track the platform globally it is necessary to refine the estimation of the camera poses and 3D locations of the feature points, which is commonly done by utilising bundle adjustment; however, existing software packages providing such methods do not take the specific problem geometry into account, and the result is a physically inconsistent solution. We develop a bundle adjustment algorithm which incorporates the planar motion constraint, and devise a scheme that utilises the sparse structure of the problem. Experiments are carried out on real data and the proposed algorithm shows an improvement compared to established generic methods.

In this paper, we consider a mobile platform with two cameras directed towards the floor. In earlier work, this specific problem geometry has been considered under the assumption that the cameras have been mounted at the same height. This paper extends the previous work by removing the height constraint, as it is hard to realize in real-life applications. We develop a method based on an equivalent problem geometry, and show that much of previous work can be reused with small modification to account for the height difference. A fast solver for the resulting nonconvex optimization problem is devised. Furthermore, we propose a second method for estimating the height difference by constraining the mobile platform to pure translations. This is intended to simulate a calibration sequence, which is not uncommon to impose. Experiments are conducted using synthetic data, and the results demonstrate a robust method for determining the relative parameters comparable to previous work.

In this paper we consider a mobile platform with two cameras directed towards the floor mounted the same distance from the ground, assuming planar motion and constant internal parameters. Earlier work related to this specific problem geometry has been carried out for monocular systems, and the main contribution of this paper is the generalization to a binocular system and the recovery of the relative translation and orientation between the cameras. The method is based on previous work on monocular systems, using sequences of inter-image homographies. Experiments are conducted using synthetic data, and the results demonstrate a robust method for determining the relative parameters.